"seem right" and "seem normal" are, alas, two different things. Right or not, it's pretty normal.
I've done this twice (once for a botched robbery on my daughter's Jeep*, and once for a mower-flung stone on my own). Because your glass is already smashed, it's not that hard to do. It's been a few years, but as I recall, once you have the inner panel off, and all the old glass cleaned out, you can simply remove the retaining clip below the glass, and slide the new glass up into the rubber gasket. I think you'll find once you open it up that you won't have to remove the window channel, etc., although this is what the service manual says.
*She lived in Boston. They broke in, jimmied the ignition lock, and tried to steal it. Unbeknownst to them, she had the fuel pump relay in her pocket.