'Now I wasn't quite sure whether Chibnall was praising GDL's performance as he cried, or he was saying it had been GDL's idea to cry. If the latter, that's a really scary thought -- the crying made that flashback!'
Oh yes, take out that crying scene and the whole flashback is completely different.

Here's what was said in the article '...Gareth [David-Lloyd] added a wonderful depth to it, when, unseen by Jack, he starts to cry at the end.' Magazine Article

I always took that to mean that Gareth improvised the crying. It wouldn't surprise me, he seems to really 'get' Ianto as a character even when the writers don't.