I think plants acclimate locally once they are established, regardless where they are. Once they feel that appropriate temps they will grow, or once gets colder time to sleep. Or the other way around, if it is way too hot, they will slow down their growth as if dormant but actually slowed down pace.
The amaryllis as far as I have tried it, sure, they can be forced to bloom in winter, but afterwards, their natural cycle to bloom is Spring.
