There's a tendency to dismiss entirely the Vandal regime in North Africa on account of the hostile literary record from writers including Victor of Vita and Isidore of Seville, as well as the relative paucity of written evidence (and of legal documentation) from the period of their rule. This is, however, misleading to an extent. The Vandals were a much smaller ruling elite than other Barbarian successor states (estimates vary but are usually below 20,000 men, women, and children), and their control over North Africa wad gained only gradually. But the numismatic record attests to the fact that the Vandals were issuing coins much in the same way as their Roman predecessors; It is the opinion of scholars such as Merill & Miles (whose co-authored work, The Vandals, is an excellent introduction to the topic) that there was a significant amount of continuity with the previous regime.

However, with regard to the control of the Vandals, I'd further highlight the fact of the Vandal persecution, the focus of Catholic denunciation. While such authors (Victor of Vita is the chief example) denounce the barbarity of the Vandal persecution of non-Arian Christians, I'd argue that the very fact that their persecution (although almost certainly overstated) is so well documented attests to their success in carrying it out: in other words, despite their weakness in numbers, they were clearly able to decisively assert their authority, at least in the later fifth century (as problems began to emerge in the sixth).

Like most barbarian kingdoms, there does appear to have been some tension with the previous ruling aristocratic class: again this is a focus (although certainly exaggerated) of Vita. But the Vandals had been living in a semi-settled state in eastern Spain for several decades at the time of their migration: though we can only hypothesise as to their adaption to settled rule, it seems likely that they were at the very least accustomed to the pattern of North African life at the time of their arrival there: about their experience in Spain in the early fourth century, we don't really have an appropriate amount of evidence to speculate.

Unfortunately it's difficult to give any comprehensive answer concerning the Vandals given the lack of documentary evidence: but I hope this provides some food for thought on the topic!

First and foremost, apologies for the couple of days delayed response. It's been one of those weeks at work (nuff said). As /u/Bakuraptor notes, Vandal North Africa is one of the more poorly documented periods in Late Antiquity. However, from the documentary evidence that survives, we can trace a rough outline of trends during the ‘Vandal Century’.

North Africa is an interesting case, given its fiscal importance to the Western Empire the role it’s wealth would play in the creation of the Vandal kingdom. The region fell rapidly within a decade of Vandal arrival on the continent, culminating in 439 with the conquest of Carthage and the seizure of the provinces of Africa Proconsularis and Byzacena (roughly modern-day Tunisia). North Africa at that time was the wealthiest region of the Western Empire, and the surplus of grain and oil formed the basis for the Roman annona, the grain-dole that fed the city of Rome and formed a large part of the annual budget. Arguably, 439 is the turning point for the Empire in the West (to the extent such points are useful), as it broke the Rome-Carthage tax spine and cut of the imperial administration from a crucial source of tax revenue. It also deprived many among the aristocratic and senatorial elite in Italy of their extensive land-holdings in the region, which they had managed in absentia.

Those who benefited, of course, were the new Vandal elite, who found themselves in possession of an almost obscene amount of wealth. For the first time in centuries, the surplus would stay in North Africa and would remain in the hands of the new elite. By and large, the administration of the provinces seems to have remained largely intact, staffed by Roman North Africans who continued to be paid in money or in kind, just as they had been before 439. There were of course, changes in job duties; the proconsul could no longer effectively act as the governor of the province (replaced instead by the Vandal king). There also seems to have been a slip in the efficacy of taxation as the century progressed as well as a decline of city autonomy in tax collection –likely in favor of a more centralized approach— and record keeping, but for the most part, the mechanism for provincial-level tax raising continued to operate under the Vandal regime, who certainly had a vested interest in making sure everyone paid their taxes.

Not only did the Vandals follow imperial models in the collection of tax, it would appear that they spent in Roman ways as well. With the exception of a decline in city forums, there is a little change in the material culture of North Africa at this time. The Vandal elites built churches and luxurious homes and palaces. The Vandal kings spoke Latin and issued coinage that was a unique blend of imperial and Germanic influences. That is not to say that the Vandals completely abandoned their own identity. They were still understood as distinct from the local population, most notably by their Arian faith. Even in this, their hard-line approach on religious doctrine mimicked Roman practices. When King Hunneric issued a decree against the Catholic heresy of the Roman population in 484, it was a deliberate echo of the language used in the legislation deployed by the Emperor Honorious in 410.

Among these continuities, there is one crucial break from the administration of their Roman predecessors. While the documentation is a little shaky, the Vandal army seems to have settled lands that once belonged to the imperial fisc or the absentee senatorial landlords, effectively creating a landed, militarized aristocracy. When this happened is up for debate, as the evidence surrounding the how is hazy and poorly document, but it is an important break from Roman practice and is a surefire sign that we are slowly exchanging Late Antiquity for something more medieval.

If you have any follow-up questions, feel free to ask!