That theory comes from a thing where some think tank that Bill / Melinda Gates foundation supports with funding (among many others), were tasked to come up with a record-keeping system for vaccinations in parts of Africa where people are illiterate and they don't have electricity. So deep tribal lands basically, and you want to immunize them with pretty much any vaccines.
So, this think tank came up with an idea - entirely theoretical at this point - that you could use bio-luminescent dyes, and a nub on the syringe which leaves a small pattern of the dye under the skin, that lasts for a few years. So, there would be a dye which means MMR vaccine and you can scan someone's arm with UV light and read the pattern and tell if they got the MMR vaccine within the last few years.
The notable point about this whole idea is that it does away with the need for central record keeping or having to keep track of people in a database, since you can treat them anonymously. The injection is the record, that's what this means. The point here is that think tanks are given problems and their job is to come up with solutions that solve the problem, and in this case they came up with this hypothetical idea of the syringe leaving a small pattern of bio-luminescent dyes as an alternative to having to ID everyone and keep track of people in a database. Consider that in areas with no infrastructure, porous borders, conflict, refugees such as system of anonymous vaccine markers would be invaluable for providing better health outcomes.
So, even if implemented as described, this is not a tracking system. The whole point is that it's for places where you can't do traditional record-keeping and there's no electricity, so the idea that this would be linked into some sort of tracking system for individuals is irrational. This is basically an extension of what they already do with voting in many remote third-world areas, which is to make you press your thumb into some ink as a mark that you voted already.