Yes, summoned monsters are subject to Globe of Invulnerability, can be dispelled, detect as magical, etc. Do keep in mind that called creatures are not - see the details of the Conjuration sub-schools. If the spell is ongoing, it's simply suppressed while in the globe (the duration continues to go on, and the spell comes back if it moves outside the globe).
Unless, of course, the Summon spell is already in effect when the globe is created, just like every other spell, per the rules of the Globe.
It's not really that confusing, it's just that there are several cases.
Existing - In Place. You create the sphere in an existing spell's area, like a wall of fire on top of you. No effect, the wall of fire is still there.
Existing - You Move. You create the sphere and move it onto some existing spell, like a wall of fire. No effect, the wall of fire is still there.
Existing - They Move. You create the sphere and an existing spell moves into it - a summoned creature or a flaming sphere or whatnot. The spell is not affected and it gets you, as it is a "spell[s] already in effect when the globe is cast".
Newer - In Place. You create the sphere and someone tries to pop a wall of fire or whatnot on top of you. A wall of fire appears with a spherical hole in it. The spell just doesn't function within the sphere.
Newer - You Move. You create the sphere and someone else casts a spell like wall of fire. You move into the wall of fire and the sphere suppresses it within its radius.
Newer - They Move. You create the sphere and then someone casts a spell that moves into it - a summoned creature or a flaming sphere or whatnot. It's suppressed while within the sphere. You can skin that as "can't enter the sphere" or the slightly weirder "it disappears, then the caster moves it back out and it reappears?"
The spell makes no distinction about whether the globe is moved onto a spell or a spell moves into it or whatnot. The net is that any spell preexisting is unaffected and any newer spell can't come into the sphere under any circumstance.