The sprocket is bolted solid to the hub: no freewheel, no brakes. You slow down purely by pushing back against the pedals — on the track that's the rulebook, not a style choice.
The condition that explains everything: as long as the rear wheel turns, the pedals turn with it — you simply cannot stop pedalling. That is the biggest adjustment for anyone arriving from the road. You slow down by letting your legs run along as dead weight for a moment and then gently increasing resistance against the pedal motion; cadence and speed drop together until the bike almost rolls to a halt by itself. The typical mistake is locking up abruptly instead of building resistance smoothly — the second is loose straps, since all of your braking force runs through the foot. What often goes unnoticed: the spectacular skid, a deliberately locked rear wheel, is advanced training and not an emergency brake. Your first weeks belong to fine modulation on the flat inner track, long before the first banked turn.