I know that they’re just tales, but I’m curious as to what time they were meant to take place in. I know that part of the Mabinogion mentions Cassivellaunus, but I always assumed that the tales were earlier than the Iron Age in origin. How possible is it that Cassivellaunus was just added in as a contemporary king?
The simple answer; we're not really sure. Also probably from a few different time periods. But, there are several key clues which point to an answer.
The four branches (Pywll, Branwen, Manawydan, and Math) are likely to all be set around the same time, as the characters often move between them. The setting appears to be (for the most part) prior to the Roman invasion. Bran, a Welsh/ British King, rules from London, suggesting that this is a time before the Romans arrived. He is also, as you rightly mentioned, usurped by Cassivellaunus whilst Bran is rescuing his sister. This, along with the general legal and societal structure, supports the idea of an early date.
However, there are several instances in the tales which point towards a slightly later date. For example, Bran rules from London, a city which (despite claims from tales such Lludd a Llefelys ) derived its name from the Roman Londinium. Secondly, in Manawydan, frequent journeys into England treat it as if it were a trip to the otherworld; to a strange and unfamiliar place. This would suggest that England and Wales were separate identities, a possibility which is contradicted by the extent of Bran's kingship. It is likely though that instances such as these are the result of later authors inserting their own bias into the tales.
The other tales are somewhat more spread across history. Breuddwyd Macsen Wledig can be more firmly dated to the 4th century, as it follows the stories of Magnus Maximus who was an Emperor of Rome in the 380's. Lludd a Llefelys is complicated in a similar manner to the four branches; although it suggests a time period prior to the Roman invasion in which Britons ruled Prydain as a whole, it also includes the the story of the two fighting dragons, which appears to be referencing a legend associated with Vortigern, a 5th century ruler of Britain (See the Historia Brittonum, or Historia Regum Brittaniae). Thus, there is no clear cut date for LL either.
Moving into the Arthurian material, things actually become slightly clearer. The three romances (Peredur, Geraint, Owain) are all clearly set in a chivalric and courtly Wales, which reflects continental courts of the 12th-14th century (aka the High middle Ages). Culhwch ac Olwen is clearly earlier; it retains a lot of material normally present in the epic Heroic tradition and very little of the courtly trappings that categorise later romances. It is likely that this was intended to be set in the "Arthurian Age", probably around the 5th-6th centuries (so slightly later than the four branches). Breuddwyd Rhonabwy is set in two time periods; the story begins and ends in the 12th century reign of Madog ap Maredudd, but the central part of the tale (the dream) is set in the indeterminable "Arthurian Age", made increasingly indeterminable by the absurdity of the dream.
Of course, none of these stories were copied down until the 11th century at the earliest, so though they may have been set in an earlier time period, they also contain elements of history and society contemporary to the redactor, which can somewhat complicate matters.
Although I am unaware of any work which specifically answers your question in further detail, I would recommend looking more into legal and societal markers as pointers for their setting. Some further reading you may find interesting:
Sources
Davies, S., The Mabinogion, (Caerdydd, 2006)
Geoffrey of Monmouth, Historia Regum Brittanniae, (1136 - the Penguin translation by Lewis Thorpe is the best translation IMO)
Dumville, D., The Historia Brittonum, (1985- you can also find a few good translations online!)
Bruford, A., Gaelic folk-tales and mediaeval romances : a study of the early modern Irish 'romantic tales' and their oral derivatives, (1969)
Me: 2.5 Degrees in Medieval Welsh, including a PhD which is two thirds done (and on the setting of the Med. Welsh Arthurian tales).