Firstly, I should like to say that this is an excellent question. I would like to have answered it earlier, in the hope that other flairs might have seen it and offered input. I will therefore endeavor to offer as best a response as possible.

Your initial statement is largely correct. During the Principate (especially in the earlier period), the army did engage in “targeted recruiting” from non-Roman groups believed to exhibit a strong martial tradition, such as the Batavians. Indeed, most auxiliary units appear to have been drawn initially from a single principal “ethnic” group. Over time, as units were transferred throughout the Empire or otherwise moved away from their initial location, recruits came to be primarily drawn from a unit’s locality, thus slowly eroding this “ethnic” identity (although unit names were still retained, even if it no longer reflected the ethnicity of the soldiers). That said, specialist units often continued to be recruited from their home provinces, even when stationed throughout the Empire. Such units included, among others, Batavian cavalry (who, growing up near the mouth of the Rhine, were famously able to ford rivers by swimming beside their horses). Such specialized units were unique, and constituted only a small portion of the auxilia.

Throughout the Principate, the differences between the auxilia and the legions became less and less pronounced. Both came to be overwhelmingly comprised of provincials, and came to be equipped in a similar fashion. The stark differences in equipment evident in iconography like Trajan’s Column (and perpetuated by Hollywood) is an artistic convention. The Edict of Caracalla, which in 212 A.D. granted Roman citizenship to all free (male) inhabitants of the Empire, also removed a significant legal difference between the legions and auxilia. Indeed, the idea of the auxilia as a seperate corps dissapears during this period. The third century is a problematic period in the development of the Roman army. The army changes greatly over the course of this period, especially in terms of appearance (in terms of equipment and clothing) and organization. While some of these trends, such as the increased use of smaller units (legionary detachments roughly the size of an auxiliary cohort known as vexillationes), can be traced throughout this period, the precise motivations for other changes cannot be so easily identified, due to a lack of source material. While it is clear, for example, that several centuries of interaction with non-Roman peoples did influence changes in military clothing and equipment, identifying specific influences is often difficult (though this has not stopped scholars from trying; Simon James, for instance, demonstrates clear Persian influences on the construction of Late Roman helmets).

In terms of organization and equipment, the army of Late Antiquity is quite different from that of the Principate, and the lack of sources makes elucidating these differences difficult. The army of the fourth century is shaped principally by Diocletian and Constantine, who reorganize it (above all else) to protect their position on the throne. Throughout the third century, Emperors came to command armies with a much greater frequency, as it became difficult (evidenced by the large number of emperors of this period assassinated by disgruntled subordinates) to entrust to another significant military forces. Emperors came thus to personally command and surround themselves with a sizeable expeditionary force, known as the comitatus. From this title comes comitatenses, the distinction by which all Late Antique field army units were known, even if graded palatini. With the establishment of the Tetrarchy by Diocletian, Maximian, Augustus of the West (285-305), and Constantius Chlorus, his deputy, or Caesar (and father of Constantine) came to strengthen their personal comitatus. It is from this period (the late third and early fourth centuries) that the first records of regiments graded auxilia palatina emerge.

Like many auxiliary units from the Principate, auxilia palatina regiments appear initially to have been drawn largely from defeated Germanic tribesmen. According to one of the Panegyrici Latini (author unknown), in the winter of 289/9, a contingent of Alamanni attempted to cross the frozen Rhine, but in the midst of their crossing the ice broke, trapping them on an island. Upon hearing of their predicament, Constantius dispatched the river fleet to surround them. According to the terms of their surrender, the Alamanni were required to hand over a number of warriors as recruits for Constantius’ comitatus. As per their enrollment in the emperor's escort force, the unit comprised of these warriors was graded as an auxilium palatinum. Michael Speidel identifies this unit as the auxilium palatinum regiment known as the Regii who, lead by their king, Crocus, were instrumental in Constantine’s proclamation as emperor following the death of his father in York in 306. The Regii are the earliest unit of palatini that can be identified. Their designation as palatini is telling, and describes their role in the overall organization of the army. Palatini, (“of the palace” or “palace units”), comes to refer to new regiments raised to strengthen the emperor’s field armies, as the comitatus, in the broadest sense of the term, came to be regarded as the emperor’s “guards” (or more pointedly, his ultimate guarantor of power), even if specific units, rather than the comitatus writ large, acted as the emperor’s personal bodyguards. That the title palatini is unknown prior to the Tetrarchy suggests that the auxilia palatina were a new class of units raised by Maximian and Constantine to strengthen what had become the most important branch of the army- the comitatus.

Their novelty is borne out partly by their internal structure. Auxilia Palatina regiments lacked centurions or optiones, having instead as under-officer ranks circitor, biarchus, centenarius (which may have been the equivalent of a centurion in traditional regiments), and ducenarius. The exact functions of these ranks (and their equivalence, if at all, with older ranks) is unclear, thanks to a lack of source evidence. Why such a new organization was employed is equally unclear. Compared to the army of the Principate, the Late army is much more poorly documented. This new rank structure existed only in auxilia palatina units for the next few centuries, and existed simultaneously with other internal organizations which, if the Strategikon is to be believed, gradually became standardized over the course of Late Antiquity.

The units of auxilia palatina raised to strengthen the comitatus of Maximian and Constantius were thus new regiments, organized differently than existing regiments, and comprised exclusively of non-Romans (unlike the rest of the army). Bound by ethno-cultural ties (or, in the case of the Regii, service to their king, Crocus), these regiments of Alamanni, Franks, and other non-Romans would have likely stayed together during their service in the Roman army, their personal ties strongly influencing unit cohesion. During this period, it is likely they would have been kept to strength with similar recruits; for example, the Regii appear to have been supplied with largely Alamannic recruits. The auxilia palatina thus initially bore much resemblance to their old auxiliary counterparts, at least in terms of having an initial “ethnic” character, although their designation as “guards” was novel, as until this time, the Imperial guards had largely lacked foreigners. It is unclear why Maximian and Constantius looked to non-Romans to comprise their new regiments. Although recruitment into the Late army is a debated topic, native Romans continued to supply the vast majority of recruits throughout the fourth century, so a lack of internal recruits is clearly an insufficient answer. Germanic tribesmen continued to be well-regarded as potential recruits throughout Late Antiquity, though they were never immediately favored over native Romans.