Does 2 PLAYER Evolution Tycoon save?
Yes when you leave. The rebirth panel says so. Rebirth itself resets you to Wood.
Saves
Leaving saves. Rebirth wipes back to Wood. Badges stay on the Roblox account.
Updated

The Roblox description shouts that the game saves progress. The Rebirth window repeats it at the bottom: “Your base progress saves even if you leave and come back” (JstlU1JvSJw@01:24, same panel in FwYAeJXiwVc@05:44). That is the leave-and-rejoin case.
The same window says rebirthing resets stage, points, and buttons back to the Wood base. That wipe is the prestige. Do not treat a rebirth as a crash.
Buy X2 Production at 1,000 on Wood (NTpIShvbpW8@01:25). Leave the experience. Rejoin on the same account. If that pad is gone and the conveyor is still running, the save did its job. Do this once after a 50,000 Base Upgrade so you are not guessing at 1am.
Wait until the plot finishes loading before you buy again. A half-loaded floor can look like a wipe.
Roblox badges stay on the account even if you rebirth. Greek at 69.1% is an account stamp. It does not freeze your Wood floor after a prestige. Sci-Fi at 9.0% is the stamp that matches the rebirth unlock sentence, but you still sit on Wood pads after you confirm.
The description does not say both friends keep identical pad states if only one is in the server. If you care, both rejoin once after a 50,000 Base Upgrade. Codes are per account either way: a used 20k on one Roblox login does not consume the other.
Code Rainbow write-ups used different persist rules, fruit storage, and Wren’s Chest. Different place ID (3017870574). Do not import those paragraphs into this remake.
Confirm 125496078313264 and Blackbox Tycoons. Rebirths: 0 on the panel means you have not prestiged, so a missing pad is a load or claim problem, not a prestige. OP.GG listed VIP servers as not allowed on an 18 Aug snapshot, so a private server is not the documented fix.
If you rebirth’d on purpose, Wood pads (X2 Production 1,000, X2 Speed 10,000) coming back is expected. That is the reset the panel advertised. The Rebirths counter should tick up from 0 and show the new +20% / +5% totals. If the counter stayed at 0, the confirm did not fire.
FAQ
Yes when you leave. The rebirth panel says so. Rebirth itself resets you to Wood.
Roblox badges are account-wide. The plot pads are not.