Aye, you seem to confuse puppets with spherelings.
The sphering process grants quite significant relation benefits, making the nation more friendly towards you (which is why you will usually get an alliance offer once they are in your sphere), but the primary reason to sphere is the economic impact or unification decisions.
It is also not always benefitial to sphere nations. The reason why China has been split up into small substates is that a unified China causes intensive problems on the world market - all the chinese pops suddenly got access to the world market, buying the products of a GP, leaving nothing for the rest of the world, causing massive ressource and goods shortages that could trigger a global economic collapse. So don't sphere high-pop nations unless you know that your industry can handle it.
The sphering process grants quite significant relation benefits, making the nation more friendly towards you (which is why you will usually get an alliance offer once they are in your sphere), but the primary reason to sphere is the economic impact or unification decisions.
It is also not always benefitial to sphere nations. The reason why China has been split up into small substates is that a unified China causes intensive problems on the world market - all the chinese pops suddenly got access to the world market, buying the products of a GP, leaving nothing for the rest of the world, causing massive ressource and goods shortages that could trigger a global economic collapse. So don't sphere high-pop nations unless you know that your industry can handle it.