Short version first: a bruise that tracks down the arm and a puffy hand in the first few weeks are both very common after a shoulder replacement, and on their own they are not a sign that anything has gone wrong. The reason you did not get it with the total and did with the reverse is mostly luck and plumbing, not a warning. Every shoulder bleeds a bit into the tissues after surgery, the arm then hangs in a sling for weeks, and gravity carries that bruising downhill through the loose tissue on the inside of the arm, so it shows up at the elbow, then the forearm, then the wrist, days after the operation and nowhere near the cut. It fades through exactly the colours Derek describes over roughly 2 to 3 weeks. Mine reached the elbow and stopped; some people's reach the fingers.
The hand swelling is the same story. In a sling the hand sits low and still, the muscles that normally pump fluid back up the arm are not working, and so the fingers puff up, worst first thing in the morning. What surgeons and physios generally ask for, and this is the bit you have got the wrong way round, is that the hand, wrist and elbow keep moving from day one: opening and closing the fist, bending the wrist, straightening the elbow out of the sling a few times a day, and resting the hand up rather than dangling. The sling protects the shoulder repair, not the whole limb. How that fits into the first weeks is set out in the week by week recovery. Your own protocol is the one that counts though, because a reverse can have its own rules about how far the arm comes out of the sling, so check with your physio what they want rather than take it from me.
Now the line you asked for, because it matters more than the reassurance. The ordinary version is a bruise that is fading and a hand that is puffy but soft, moves, and is better once you have been up and moving. The not ordinary version is any of these: a whole arm that is hot, tight, red or painfully swollen rather than just puffy at the hand; a deep ache in the arm that is getting worse rather than better; fingers that are going numb, tingling, cold or pale; a fever, or a wound that starts to weep or redden; or pain in the shoulder that is climbing day on day rather than easing. Any of those is a same day call to your surgical team, not a forum question. Blood clots are rarer after shoulder surgery than after hip or knee, but they are not impossible, which is why the hot, tight, whole-arm swelling gets named specifically. And because yours is a reverse, one more thing that is nothing to do with bruising but belongs in the same conversation: a sudden clunk or give in the shoulder with the arm no longer lifting is a different problem entirely, and dislocation after a shoulder replacement explains what that looks like so you would recognise it. From what you have written, you are describing the ordinary version. Your wife is not wrong to want it looked at, and a quick photo to the physio or a call to the ward is a perfectly reasonable middle road.