My tenant just paid me August rent that is about 50 days past due. Should I get him evicted?
Any payment for back rent is an offer to settle a potential eviction. If you received the payment, you effectively settled your claim to eviction for this rent period. You can still sue for back rent, but you can't evict for now.
If you want to evict him, you'll have to wait until the missing of Oct. 1 payment, and refuse to receive any back rent until he's evicted.