From my investigations, it looks like zsh performs <> substitution before $ substitution. That means when you use the $ variant, it first tries <> substitution (nothing there) then $ substitution (which works), and you're left with the string containing the <> characters.
When you don't use $manuals, it first tries <> substitution and it works. It's a matter of order. The final version below shows how to defer expansion so they happen at the same time:
These can be seen here:
> manuals='/usr/share/man/man<1-9>'
> echo $manuals
/usr/share/man/man<1-9>
> echo /usr/share/man/man<1-9>
/usr/share/man/man1 /usr/share/man/man2 /usr/share/man/man3
/usr/share/man/man4 /usr/share/man/man5 /usr/share/man/man6
/usr/share/man/man7 /usr/share/man/man8
> echo $~manuals
/usr/share/man/man1 /usr/share/man/man2 /usr/share/man/man3
/usr/share/man/man4 /usr/share/man/man5 /usr/share/man/man6
/usr/share/man/man7 /usr/share/man/man8