tmux has an option, mode-keys , you can find it on the manual page.
default is emacs , but if your $EDITOR is vim / vi, tmux will use vi .
So, key binding will be in vi mode.
eg. your Alt-w will not work, this is emacs binding. you can see the key binding table on the tmux man page.
Some of them are related to your question:
Function vi emacs Copy selection Enter Mw Start selection Space C-Space
so you have to go with vi-mode keys.
I also used vim mode and made a little tweak (to make it the same as vim) in tmux.conf, maybe you could try:
bind-key -t vi-copy 'v' begin-selection
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