star trek - How did Voyager return to the Alpha quadrant?

Maybe I missed something, but Seven of Nine clearly responds to a question of how long until the nearest conduit exit, with:

30 seconds away, but it will deposit us back to the Delta Quadrant.

Then:

A Borg sphere swallows Voyager while inside the Transwarp conduit, which proceeds to exit into Alpha quadrant. Voyager then fires a torpedo while inside and suddenly the Borg sphere explodes and they're all free in the Alpha quadrant

So to be blunt, how did Voyager return to the Alpha Quadrant, when clearly they said they were exiting back to the Delta Quadrant?

Answer

I think you misheard or mis-interpreted the dialogue. Chakotay asks, "Where's the nearest aperture?" In other words, the nearest opening, so they can escape the transwarp conduit before the Borg sphere destroys them. That's when Seven says, "30 seconds away, but it leads back to the Delta Quadrant."

This puts them between a rock and a hard place: their armor won't last with the sphere firing at them, and if they exit the conduit, they end up back in the Delta Quadrant. Naturally, they focus on Janeway, with a tough decision to make (knowing that if they go back, which is safest, the network of conduits will not be there for them to use again) and then they cut to another scene.

From there, we see Federation space, with many ships all ready for when the Borg ship comes through and a Borg sphere emerges from the conduit. Then we see the Voyager bridge. Janeway asks Paris, "Where are we?" Paris says, "Right where we expected to be." Then she looks at Tuvok and says, "Mr. Tuvok?" He fires a torpedo that destroys the Borg sphere.

Their armor is strong enough to survive this and leave them there after the sphere is destroyed.

Obviously, you've filled in what happened, at least to a point. With depleted armor, Janeway lets the Borg Sphere pull them in, which means they'll stop firing on the Voyager. The sphere continues on its way to the Alpha quadrant, with Voyager captured in it, not knowing their captives have enhanced weapons that can blow away the sphere.

The misunderstanding seems to be that it sounded to you like the only course open was another conduit back to the Delta Quadrant. It wasn't, it was the only escape route that would get them away from the Borg sphere.