The deal isn't secret. He got to keep his life for now and the wagner troops avoid treason trial. Remember it isn't only about Prigozhin. When the actual Wagner troops heard Putin call them traitors, their rebellion enthusiastic might have lapsed greatly. Since one part of the messaging seemed to indicate the plan was This isn't about Putin, but military high command. Dear Tsar, your boyars are misleading you. Not to worry Tsar, we are here to help. Well Tsar decided to side with boyars, so now it was open rebellion against Tsar Putin and He just ruled all of the troops rebelling national traitors. Did prigozhin actually order Wagner to stop or did Wagner troops refuse to continue.

Probably Prigo got some money as part of the deal, since that is how Russian kleptocracy works. Everything is greased with some money. Exile, keep life and some wound healing money. Thing is Prigo is probably dead man walking. The safety assurances he got are worth nothing. However it might have been "take this deal or bullet to head immediately". Maybe you die later, maybe you don't. If you don't take the deal, you die certainly immediately. Kremlin just didn't want massive blood shed at gates of Moscow for PR, so offered a deal.

They got to 100km from Moscow and there they had Kremlin regiment and other Moscow defense zone troops vanguard waiting saying "you come closer, we start shooting. Our bosses message is stop here and bygones be bygones. Continue and there will be no mercy for you."

They got to just drive on in the hinterland, since there was no troops there. Moscow is different matter. It has permanent anti-coup/anti-decapitation garrison. Multiple regiments worth of it, so not just couple hundred ceremonial guards. Thousands of troops in garrison. Given it was only finally 5K Wagner troops driving to Moscow, most likely they were actually out numbered even by the permanent Moscow garrisons. Plus airforce close air support on top of that (even if Wagner had manpads).