Follow up vs. follow up on

I guess this might not be the first time someone has asked this on this forum, but as I couldn't find it with the search function on the left upper corner of the page, i am posting it as a new question here.I get confused about the following usages "They followed up their recommendation with concret proposals""I am following up ON our last correspoendence""They followed up the issue from the last meeting and ...""He followed up ON the issue from the last meeting with ..."They all seem okay to me but I wonder how a native speaker would view them.One of the online dictionaries states the following"follow up (tr, adverb)" This implies "follow up on" is not right.Any help? Thank you.