I'm not sure if we understand completely the magic, but people have mentioned the regeneration genie giving them a visit
Regeneration happens when the string slides faster than the velocity at the surface of the tip, so the friction force is in the direction that speeds up the top (let's call it "positive friction"), or at least at the same speed (rolling condition).
When I first developed the diabolo tip (independently from Salvador who came up with the same design), my theory was that if I got the neck of the tip smaller, the tangential velocity would be slower and it would be easier to achieve positive friction with the string. In hindsight, perhaps the biggest benefit was that the "negative" friction (when the string didn't slide fast enough) was lowered. This is specially true for on-string regenerations.
A top that has more rotational inertia (e.g. bigger) would also spin slower, so achieving positive friction should also be easier. However, you need more torque to spin a more massive top, so it can be detrimental if the size of the neck or string are too small.
Now, Jose's top is nearly impossible to regen at very low speed
I'm not sure what's the explanation. Perhaps for regeneration you need to achieve the rolling (no slippage condition, so we are not really talking about friction), and the string is too fast.
