Not many but 'some' tweaks require a 'reboot' after installation.
Now, if that tweak isn't compatible with you're current iOS and you tap the 'reboot' on the Cydia screen, you fall into some problems that you might not get out of.
Normally, if a non-compatible tweak that requires a reboot doesnt work, the iDevice will be kicked into Safe Mode where you can uninstall the recently installed tweak ..... But for the current jailbreak, if that tweak is incompatible, it will cause such a problem.
Hacks/tweaks only require a respring when the newly installed directly affects the interface.
So when you install command-line only functionality there is no need to respring.
jailbreak apps/tweaks/hacks hook into the springboard to be able to control views that get displayed or user interactions, it requires a respring to "update" the Springboard/Settings.
Like how you need to respring every time you change a theme , it's simply to update the system, introducing the new app/tweak/hack to you're device can not be done while the device is running.
You're Qusetion was :
what do you do if you need to reboot to make the deb/hack etc work if your on a tethered device?
The answer is :
Check that the tweak is compatible with you're current iOS and reboot.