Does this happen with 6.0 as well (https://dist.torproject.org/torbrowser/6.0/)? On which platform? Is it enough loading mega.nz in my browser to see the problem or do I need to be logged in? Is the browser still working afterwards or does it crash?
Could you test that again on your machine? Taking a clean 6.0.1, going to mega.nz and then updating to 6.0.2 and doing the same (see: https://dist.torproject.org/torbrowser/ for a 6.0.1)? The fix for #19417 (moved) should prevent your problems.
Are the cached asmjs files in 6.0.2 still there after you accessed mega.nz, closed Tor Browser and restarted it?
Oh, maybe that is due to you having disabled Private Browsing Mode in your Tor Browser? (clicking on the green onion -> Privacy and Security Settings... -> Don't record browsing history or website data (enables Private Browsing Mode) would show you the latter unchecked)