No, it does not. You are confusing "until end of turn" with "at end of turn." It's a common thing to do, but there is a very important distinction.

Effects that do something "at end of turn" will trigger at the beginning of the end step. If they come into being after the beginning of that turn's end step, they will wait until the next end step (which will be the end of the next turn) before triggering.

However, both of Mishra's Factory's abilities last until end of turn. "Until end of turn" effects expire during the clean-up step, which comes after the end step. In the clean-up step, nobody gets priority (unless something triggers in which case there will be another clean-up step afterward), so you can't play any spells/abilities at that time. So, no matter when you play either of the creature-related abilities on Mishra's Factory, the duration will expire before the next turn begins.

313. End of Turn Step

313.1. As the end of turn step begins, all abilities that trigger “at end of turn” go on the stack. (See rule 410, “Handling Triggered Abilities.”) Then the active player gets priority and players may play spells and abilities.

313.2. If “at end of turn”-triggered abilities are created or if cards with “at end of turn”-triggered abilities come into play after preexisting ones have already gone on the stack at the beginning of the end of turn step, those abilities won’t go on the stack until the next turn’s end phase. In other words, the step doesn’t “back up” so new “at end of turn”-triggered abilities can go on the stack. This only applies to triggered abilities that say “at end of turn.” It doesn’t apply to continuous effects whose durations say “until end of turn” or “this turn.” (See rule 314, “Cleanup Step.”)

314. Cleanup Step

314.1. If the active player’s hand contains more cards than his or her maximum hand size (normally seven), he or she discards enough cards to reduce the hand size to that number (this game action doesn’t use the stack).

314.2. After discarding, the following actions happen simultaneously: all damage is removed from permanents and all “until end of turn” and “this turn” effects end (this game action doesn’t use the stack).

314.3. If the conditions for any state-based effects exist or if any triggered abilities are waiting to be put onto the stack, the active player gets priority and players may play spells and abilities. Once the stack is empty and all players pass, another cleanup step begins. Otherwise, no player receives priority and the step ends.