Ive had two water births. My first was in the hospital. They made me get out and lay on the bed (after the baby was born). The placenta took a while and i had lost the max amount of blood so i got the injection at that point.
My second was a HB. I birthed the baby and then i got out and laid on the bed to birth the placenta again. I didn't want the injection if it wasn't necessary. My placenta came out in 7 minutes after the baby was born (no major bleeding, it was actually very minimual). If i would have needed (or wanted) the injection, they would have just done it once i was laying on the bed and awaiting the placenta.
The majority (though not all) care providers have a water birthing mom birth the placenta on "land". This is due to several reasons, but the biggest is so that they can monitor blood loss as it's quite the challenge when water is invovled. So they know if they need to give the injection (or in the case of you wanting the injection, give it to you then as i cant imagine how an injection would work in the water)