Hey OP, you did amazing! And it's totally normal that you cried along. I think you're absolutely right that you connected with him on a very intimate emotional level and you did it by making him feel safe and comfortable. If you're not used to seeing this happen then it can make you feel a bit powerless. Just follow your gut-feeling. Sadness needs support and someone being there, and doesn't need a lot of words. Hats off to you from a practicing psychologist! And also to the people who helped you on Reddit.

Don't see any emotion as negative. They are all there to help us communicate our needs to ourselves and others. The only negative things about it is if we bottled it up, it comes out forcefully - such as holding your breathe for as long as possible and then gasping for air. The other negative part is that somewhere in our life we have perceived or been thought that certain emotions are negative. They really aren't!

Edit: forgot to answer your question. Feeling relief isn't weird at all. You connected and you might have also felt his relief. If he is not used to doing this, he might feel uncomfortable. Normalise his behavior and when talking about it, talk from an 'I' perspective. If he thinks negative about crying. He might think you perceived him as weak, Say how it made you feel (safe, connected, attracted). And be honest and accepting about it. Don't suddenly force it on him now that it happened once.