Not exactly sure how you’re asking the question. My English is not too good but I’ll try my best :P.
From my own experience of owning all seasons of deerling in BW and B2W2 the game would automatically evolve them to whatever season is in the game, because I do know that seasons in the Gen 5 main games didn’t always match up to the real season irl. But games past that I never actually tried capturing and deerling and testing it out. So if you’re talking about deerling not matching up our irl season in the BW and B2W2 games then no it can still evolve no matter what. Deerling will evolve whatever season.
Hopefully I answered your question, cheers and goodbye ^_^