PRoot/tmux: opening a new pane to the correct working directory?

In default tmux, opening a new pane will correctly open to the same working directory of the previous active pane e.g.
cd ~/test_dir
# new pane
pwd
~/test_dir


However, if I enter a PRoot via proot-distro, change to a new directory , and then open a new pane, it will open with a working directory that was active when I entered the PRoot:

cd ~/test_dir/
proot-distro --termux-home --user user debian
cd ~/test_dir/sub_dir/
# new pane
pwd
~/test_dir


Is there a way to trick tmux into opening a working directory in the proot?
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