Our washing procedure was:
With agent (broulin) Mechanic required.
First disconnect the PC line on the FCU, blank it off. Close the bleed-valve, with a choke. Pull the circiut-braker for the ignitor.
Monitor starter at 10% for 10 seconds while injecting the wash.
After the excess fluid has drained off, then repeat the procedure twice but only with clean water.
For drying.
After it has drained off, unblock the bleedvalve, connect the PC-line and ignitorbreaker and do a normal start, run for 3 min. at flight idle, open the heatervalve, and shutdown.
The reason for disconnecting the PC-line, is to prevent the agent from wearing on the membrane of the bleed-valve, almost impossible to rinse completely.
Waterwash:
Block the bleed-valve, pull ignitor breaker, rinse twise, then do a start as above. No need for a tech./mech.
In this way, I have never had water or cleaning agent entering the cabin the way you describe.
Only through the normal stardard-issue leaks provided by Bell.
Hope it helps.