I use the following mappings to perform navigation in the bug demo below.

nnoremap <space> /^    p.*(.*<CR>:nohl<CR><ESC>nnoremap <leader><space> ?^    p.*(.*<CR>:nohl<CR><ESC>

Expected behavior is that upon each jump performed, the statusline should be updated to display the function name arrived at.

Actual behavior is seen in the screenshot. My interpretation of it is that expected behavior occurs about only 10% of the time. 90% of the time, the statusline displays the prior function rather than the current function.

Other details.

1. Any time the statusline is late, any movement within the function (in the screenshot, I use '$' to go to end of line, or use which is just a trivial mapping I have to run nohighlight.) will update the statusline to the correct value 100% of the time.
2. I don't believe this is a latency issue as some other issues have been suggesting, because tagbar responds quickly to the jumps in the screenshot. The "delay" is instead in what function tagbar thinks it's currently in.