From SP or a relaxed state, in my experience the point is to lose your waking body, and focus on dream visuals, moving then into the feelings.

There's also not always a 'transition' when I enter dreams through WILD. With transitions following the visuals, then the speeding feeling, then the awareness of dream senses -- very like physical senses for a while.

Sometimes it happens that you are already dreaming. I find the longer the meditative period (without thoughts) is before entering, the greater the transition, instead of following the visuals more and then the greater the chance of being in the dream without consciously entering.

I suggest if you want to transition specifically, then use a more 'feeling' method of entering, like spinning yourself (mentally). Become absolutely just motion.
The feeling needs to be pushed a little, but it should come quite easily.

What is needed before the spinning, is to forget the body, just follow your imagination, but not too engaged, you need to lose yourself in the action, so don't think about it or yourself, but also don't go so far as to lose consciousness too.

Then when everything *stops existing* (in a sense), spin. It's a little difficult to understand at first (it seems contradictory to 'lose the body' and then spin), but when you get it WILD becomes easy.
This is not like entering from a meditative state, nor through visual imagery, it's a stronger sensation.

Once you're in, you'll probably be quite surprised and ecstatic. The excitement is good at first, so just be happy, however in further WILDs you'll get used to it and likely ground yourself for a longer lasting dream.