I'm currently reading "The Tyrants of Syracuse: War in Ancient Sicily Volume 1: 480-367 BC"

It's main focus might be a bit broad for your specific question, but the first few chapters are about the colonization of Greek and Phoenician cities in general, with an obvious focus on Sicily. All the Greek cities on Sicily were started off as colonies, first from either the Greece itself or the Greek cities that were in Asia Minor. Obviously the colony of focus here is Syracuse, and it ended up being the dominant city on Sicily and so might not have had the same relationship as many colonies to their founding cities, but you should still be able to find the info useful.

In general, there seems to be a loose association of the colony with its founder once the colony was firmly established. From reading ancient histories, it seems like the main connection was which type of subset of Greek the city was (Doric and Ionian being the main two colonizers) - for instance the Ionian league in Asia minor, and they were generally supported by Athens, who was an Ionian city itself.