Oxford Dictionary (https://www.lexico.com/en/definition/just) gives this definition about "just"
Barely; by a little.
and these examples
‘inflation fell to just over 4 percent’ ‘I got here just after nine’ ‘I only just caught the train’
I am aware that the first 2 means "by a little more", such as 4.01%, 9:02.
I have some difficulties on the last one, had he catch the train?