How does one tell if one’s Tulips are “species”? Does that refer to named varieties like Helmar or Finola?
Personally l would buy new tulip bulbs in the Autumn , but you could plant them in the garden if you are able to
I've kept them before and the best I can say is they're ok ish in the second year, but I'd rather free up the pots and spend a few quid on nice fresh bulbs in the autumn.
Most don't perform well in subsequent seasons as it's difficult to give them the conditions they need after flowering, in most areas of the UK.
The species ones are reliable, and will increase, and a few other types are reasonable in some areas. Otherwise, they're rarely worth keeping.
I live in west central Scotland - not where that photo is...