A defender following a raider into the opposite court is called Pursuit. Defenders cannot pursue when they feel like it, there are some rules to be followed.
Link to General Rules of Play:
viii. After a raider has reached his court, the opponents shall send
their raider within 5 seconds. Each side shall continue to send their
raider until the end of the game in this fashion. In case the raider
fails to start his raid within 5 seconds the team loses its chance to
raid and the opponent team is awarded a technical point.
ix. When a struggle takes place in a raid, on completion of such
raid, Rule viii (above) will not be applicable. The next raid will
start on the whistle of the referee after the out players have been
seated in the out box.
x. If a raider, who is caught by one or more defenders, escapes from
their attempt to hold and reaches his court safely, he shall not be
a. Note: But if a raider touches one of more defenders and reaches his
court safely, he may be pursued.
Per rule ix., after raids in which a struggle took place, defender is not allowed to enter the opposite court until the referee blows the whistle, so he has to wait for the referee's whistle.
Per rule x. and rule x. a., a defender may pursue a raider if raider returns to his court after touching one or more defenders, but not if he escaped from a struggle.
Other than these cases, a defending team has to send a raider within 5 seconds, they don't wait for the referee's signal.