Termina is another country, like Labyrnna or Holodrum. The portal there is in the lost woods, like the portals to Zora's River and Goron City. This is evidenced by Tingle. Tingle's (exaggerated) events in MM are recorded on the golden Tingle statues in TWW. Now, if the games fall on opposite sides of a split timeline, how did the adult timeline end up with information from a supposed parallel world in an alternate timeline? Either they're in the same timeline, and there's no split, or Termina is another kingdom and someone was assisted by Tingle and saved Termina without Link being there.
The Happy Mask Salesman obviously ran into Skull Kid, as Skull Kid knocked him out and stole the Mask. He likely got to Termina in a similar way as Link (a lost woods portal) or perhaps sailed across the sea and ended up in Great Bay, or, if Hyrule is east of Termina, which could be indicated by the Triforce markings in Ikana, then he could have traveled from Gerudo Desert and ended up in Ikana Canyon.
