Though I didn’t just simply ‘conjure it up’, I’ve considered a Phoenix named Leska as my spirit animal. It used to be a large blue bird, but over the years seemed to have ‘evolved’ into a phoenix. Leska’s colors vary. I - as you, call Leska when I’m in trouble, but they are in ND’s. I don’t know if it is the same for you or not.
I’m one to believe that your spirit guide will take the form of whatever you desire deep inside. I’ve always had a deep liking for a phoenix, (not inspired by Harry Potter). And that is probably why it is. It forms a better connection with me.
It’s been a long time since I first encountered Leska, but i believe it was a point where I was in trouble in a low level lucidity. I had always believed in an entity that existed in my dreams, though at that point I had no idea what a spirit guide/animal was. I just felt a stronger connection with it at that time, like it was calling me. I looked towards the sky, and asked for aid in desperation. I had no idea it was going to be an animal at all. I didn’t even think it would have a shape.
I guess my experience is that I believed there was someone/something there and bonded with Leska before I actually saw it.