Study Kings and Chronicles....when northern Israel split from Judah....the levites and Judah stayed south. The Northern 10 tribes were taken and scattered first. It doesn’t mean that some individuals of other tribes never stayed in Judah when the northern tribes lost their home lands and their Identitities.
Wikipedia....amazingly for them has a very good article about the 10 tribes, where they went ect.
For your edification:https://en.wikipedia.org/wiki/Ten_Lost_Tribes
Not all levites stayed south. There were Levites in the northern kingdom. In the southern kingdom you had Judah, Benjamin and also Simeon (they were surrounded by Judah and probably absorbed very early on)