It is temperature and water which govern dormancy rather than light. My pelargoniums overwinter in a cold greenhouse. Light but cool. The temperature is clearly too warm for it to remain dormant. The water you have been giving it was also a lot for dormancy. In fact it is quite a lot even for full growth. Unless you have somewhere much colder you will now just have to let it grow again. You could cut it back but without seeking the shoots I can't be categorical about that.

Got it! Much less water, and colder... Should I do that now that it started growing, or keep it in mind for next overwintering ? Won't changing temp and water at this point shock it ?

As I said, I can't be categorical because I can't see how far developed the shoots are. But probably best to get it into maximum light now it's begun growing. Still relatively cool though, if possible. When can you put it outside in your area?

I'm sorry, don't own a cell for pics. Maybe soon :)

The plant is young. A test my mom gave me, before giving me her bigger ones (which frankly, I'm not sure I want anymore if I'm going to kill them all!!).

Total height is only 6 to 8 inches. It had gone bare last December, after staying throughout Fall in a cold room (a very sunny little nook build against the house, and used to double the house door like an exterior vestibule - just like a little hothouse and the best place to keep plants throughout 3 seasons here; just not Winter when it can go down to -20).

So it is about 3, 4 branches, on which over a dozen 4" petioles and small leaves grew unidirectionally.

Saddly, as mentionned above, the geranium can only go out at the end of May. But like I said, it's been pretty warm allready, so I'm hopefull for a very warm Spring, during which the geranium could go in that nook - should be around 30 in there right now).

But, it is now about 55 degrees in the geranium's room, so I'll move it to a much sunnier, colder place... but the nook would be too cold presently, I'm sure.

How cold could the geranium stand with new growth ?