Yes it is normal. They are not separate. I found this out when my oil cooler let go as I was driving and sucked all the coolent into my tranny, good times, good times. What I did, was to take the rad out and cut sheet metal so they will just fit inside the holes. A dime might work well. I put JB weld in the hole then put in the sheet metal and filled it with the JB weld. Make sure you mix the JB weld so it is a little harder than normal, so the set time will not be as long. Let it sit and harden for whatever the package time says it is.

Or you could just take it out, bring it to a shop and they can weld up the holes.

I have put about 5000 kms on the car since I have down this and it has not poured out a drop yet. Your choice which way you go. JB Weld is cheep like me, so that way worked for me.

Good luck.
I have put about 5000 kms ont

 

I'll give it a shot this week. worst case scenario I will buy a new rad later on. thanks for the info

 

It WOULD mean that trans fluid and coolant are mixing if you had the trans cooler connected.
What it DOES mean is that the transmission cooler in the radiator is leaking, thankfully you have it disconnected but it will continue leaking coolant until you fix it.
You can replace the tank, the cooler, or the complete radiator assembly.
Doing the whole radiator is usually the most reliable long term repair, but not your only option.

Usually when I install an auxiliary trans cooler, I leave the factory one in the "circuit" to provide additional cooling. The way you did it is fine I guess, but I do it differently.