Cache clash when running two servers in same Chrome browser?

I am using a single instance of chrome in which I have two tabs, each tab points to a different sb docker server with its own url. I am "side by side" testing version 2.4.1 on port 7010 against the 2.9.0 Edge version on port 7011.

Will the two versions of sb running at the same time in the same browser cause cache issues?

The reason I ask this question is that if I used 2.4.1 in tab 1 for a period of time and then open tab 2 and test some functions in the Edge version, I find I have to clear cache and reindex the Edge version.

Should I run two Chrome Browsers with one tab only, Browser 1 runs 2.4.1 and Browser 2 runs Edge?

TIA