Both alpha 4 and nightly setup /tmp with overly restricted write permissions, preventing other users from being able to use /tmp files. Specifically, /boot/system/boot/InstallerFinishScript should probably add an additional chmod a+rwx "$target/system/cache/tmp" line.
I used to be able to work around this permissions gap by patching /boot/system/boot/Bootscript (it contained a chmod command that was nested incorrectly). But now that nightly has removed this file, I’m not sure whether it would be looked for and executed on boot anymore. In any case, /tmp permissions should be fixed by default for future Haiku installations.
Fortunately, it appears that executing chmod a+rwx /boot/system/cache/tmp does persist across reboots as a workaround for nightly, where this was not the case with alpha 4.