"riff"

Not really. Tougher skin on your fingers is important, but (as the others say) will happen naturally and steadily.
What goes with that is strength and speed in the fingers.
All 3 things (toughening, strength, speed) will come the more you play. You don't need to do specific exercises for any of them, just keep playing anything and everything. The more different things you do, the more organic and natural your whole technical skill will become.
It's difficult to know sometimes what people mean by "calluses", but - as Malcolm says - it does seem as if some beginners get obsessed with them. What you DON'T need are hard lumps of dead skin on your fingertips. They will eventually peel and drop off and you have to start all over again.
Personally (I've been playing well over 40 years), my fret hand fingertips are barely distinguishable from my picking hand. The prints are just a little smoothed out, and the skin is certainly less sensitive.
As a beginner, I do remember getting painful blisters, and the dead skin would peel, leaving tender new skin beneath - and I'd have to stop practising till it healed. But eventually the new skin (and the existing unbroken skin) got tougher and less sensitive -
without callouses ever developing.
YMMV of course. I'm just saying thickened callouses are not
essential.
Again, that's down to lack of strength, not the softness of the fingertip. Of course, if the skin is too soft, it's painful to exert the necessary strength! - which is why I say it all goes together.
Good exercises for the pinky - away from the guitar - involve strength and accuracy of impact. Try drumming with the fingertips on a desk or table top, making each finger tap with the same force - obviously focussing particularly on the pinky.
The edge-of-the-credit-card idea may help the finger(s) get used to pressing strings (rather than just flat surfaces), but don't overdo it. Don't
seek to develop callouses. IOW, don't damage the skin if you can help it.
When playing the guitar, use the pinky as much as you can for normal fretting. Eg, anything you're used to playing with fingers 1-2-3, try doing it with fingers 2-3-4 instead.
As Ian says, make sure your instructor is checking your hand position, and ask him if you're not sure. Correct hand position is absolutely critical, to give you the best foundation for improvement. Your journey has to start from the right place

.
Ask him to suggest some pinky exercises if you're concerned about it.