Did they pump out water in order to surface?

No, the water was not pumped out.  They blew the water out using high pressure air. That air was stored at 3,000 PSI in bottles in the ballast tanks. To surface, the air was stepped down to 600 PSI and dumped into the ballast tanks. Once the bridge hatch was out of the water, the high-pressure blow would be secured and the low-pressure blower was used to blow the tanks dry. The low-pressure blower was run until bubbles appeared from the ballast tanks. (The low-pressure blower ran at 10 PSI.) This eliminated the need to use any more of the stored high-pressure air.

The air used to surface the boat would be lost when they dove the next time. It was just vented so that the ballast tanks can be filled quickly.  They replaced the air in the storage bottles by running the air compressors as needed when on the surface. There was usually enough air in the bottles to surface the boat about seven times.

There were two 3,000 PSI air compressors in the pump room below the control room. The low-pressure blower was also in the pump room. The high-pressure air manifold and the controls for the low-pressure blower are both in the control room.

It was possible to surface the boat without using any high-pressure air. The boat was driven toward the surface with the planes. Once the bridge hatch was out of the water and opened, the low-pressure blower was used to blow all of the water out of the ballast tanks. It was slower, but it worked. This was done most often when training new diving officers and lookouts to submerge quickly. There was enough high-pressure air in the tanks to surface the boat multiple times, but perhaps not enough for all those training dives.