Granted, I watched the PT episodes several months ago, but I don't seem to remember any point in that storyline in which Barnabas went from wearing his coat in RT to PT without it. I'm pretty sure he was wearing it when he first travelled there in Ep #980 (repeated in Ep #981) and it made the crossover with him. And I could be wrong, but I don't think he was wearing it when he travelled from PT to RT and then back to PT in Ep #1031.
Now, one thing I do remember is that the coat definitely didn't make the journey from 1970PT to 1995RT. Though, of course, Julia was also with him at that time, so she couldn't have sent it to him even if she could have figured out how to get it 25 years into the future.
Perhaps Barn's coat arrived in 1995RT on a time-delay because it had to go through travelling-to-the-future customs.