I am currently working on the spider exercise as well.
When I was just practising with the first 3 fingers as Lisa recommends initially I had a similar problem to you.
I decided to try adding the pinky to the exercise to try and train that along with the others and it seems to be working.
The other problem I found was keeping the other fingers fairly close together and near the fretboard, which Lisa said might be a problem. That seems to be coming together as well now.
I plan on practicing that exercise about 30 mins each day for a week before doing next lesson so hopefully I should have it reasonably down, ready for next steps.
Stick with it 😊