Okay, better idea of what is going on but also more confused as it should not happen!
But I am also very confused about the labels as they do not seem correct as you are reading them and I do see that they seem to mislead! !
They do seem very strange on several points as they seem so wrong!
This is the way I would expect them to work.
View attachment 2503771
I think of drains on the waste and grey water tanks to be the big sewer hose size and coming out below the tanks using one single outlet where you connect the flexible hose to the place we drain. There should be a valve to let you first open the black tank to drain the solids and close that valve. Then there should be a second valve to open and drain the grey water through the same connectin to the dump site. Done in this way, it let us "clean/flush" any remaining solids out of the flex pipe before we store it in the RV! A bit cleaner than hauling the flex around with solid waste in it? Also the grey water tank opening has to be very near the bottom of the tank to fully drain, so a drain out the side doesn't seem correct!
Then there is the note at top right that says we only connect potable water here! This is because we use this port to fill the fresh water tank where we store the water we drink and cook with it! Good clean water only into the tank we drink from with NO connection to the waste tanks!
Then when we want to use a different hose at a drain point to flush, we have a note at top left saying to make sure the drain is open before we turn the water on to flush the tank. They give us a different hose at dump stations to avoid any chance of connecting anything we drink to anything we use for waste! If we fail to follow that yellow sign and put water pressure on the waste tank without first opening the drain, we might force waste up and into our face! That is not going to be a lot of waste if the vent is working to let the pressure go up and out but they simply do not want the chance of air and spray from the waste tank coming inside!
Never connecting any water we drink or eat with waste, is the basic main point!
So I think these labels should say there are two valves underneath, one to drain the black waste, another to drain the grey and they both have valves to let the waste go out the same main flex hose we connect to the sewer when draining. Main point on these is that it drains down using a common hose for ease of dumping both. One flex hose for two uses but only when we are dumping or flushing to finish! I read the warning at left for that connection for flushing the black tank!
The connection and label at right is for when we want to fill the fresh water tank, there is likely a vavle at the wet bay to send water to the tank or let us use the water inside by setting the valve to send it to faucets!
I'm not certain about there being a valve but I am guessing there is one to direct the water to the tank or for direct use from the hose.
But for the question of water forced out here when using the pump? There should normally be a check valve to keep water from the fresh water holding tank from going backward through the pump. Also there is usually a check valve built into the back side of this port to keep water from being forced out and down the RV side!
Note that the place where we connect the dringing water hose has a flap with stopper to keep things like bugs from going into that pipe where they might live in our drinking water? Good to keep that covered!
I think the bad label placement may be confusing you but if water tends to come out this hose connection when using pump, the check valve here may need a look.
Another small note to warn about high pressure if getting near mountains, etc. where pressure can be extreme?
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See if that fits what you find and wish you luck on the new adventures!!
Hope it helps and solves some problems.
I am certain that MOST Americans do value our Canadian neighbors.