Look, bro.
You are pulling this log from the wrong end. Guessing will never help you.
There is a thing called error message.
And you desperately need to get in touch with it.
It will tell you everything of the reasons why your sessions doesn't work.
If it's really a /tmp problem, PHP got a special error message for tis case:
Warning: Failed to write session data (files). Please verify that the current setting of session.save_path is correct (/tmp))
If you get this message, you can be certain that it's the reason for your sessions doesn't work and you can start to repair it.
It has an error message for the wrong session handler as well. As well for the every other problem.
So, you have to get error message first. Then read it nd it makes you know, what certain problem you have. Easy-peasy.
As a quick workaround you can use this code to bring error messages on the screen
error_reporting(E_ALL);
ini_set('display_errors',1);
but only to debug this situation and then remove it. Error messages shouldn't be output on the screen a production server.
So, learn to read error logs. I am sure your server put all errors messages into error_log. Just find it and look for PHP errors.