In most cases yes, the ticket is issued straight away. For low cost airlines the payment and the ticket happen in the same step, so the moment your customer pays, the seat is bought and the airline reference comes back to your portal within seconds. Your customer gets the confirmation there and then, and nothing is left hanging.
On some fares, mostly the ones that come through a global distribution system, the booking is made first and the ticket is issued as a second step. The airline holds the seats under a booking reference and gives a time limit by which the ticket must be issued, which can be a few hours or a day or two depending on the fare and the route. Your portal can be set up to issue automatically as soon as the payment clears, or to leave that step to your own staff so you can check the booking before the money goes out.
Be aware that the time limit is set by the airline, not by us, and it is real. If the ticket is not issued before it runs out, the airline cancels the booking on its own and the seats go back on sale, sometimes at a different fare. So if you choose to issue manually, someone in your office has to watch the pending list every working day.
Decide which of the two suits you, automatic issue or a manual check, and ask us to set your portal that way, then keep an eye on the pending bookings screen for the fares that do not issue instantly.