Can one fasten the schach mats to the walls with plastic ties as a precaution not to fly of even though there are 2 by 4 beams on top of the schach?
It is permitted. Normally we are not allowed to support the schach with something that is “mekabel tumah” and plastic ties are considered a kli and are mekabel tumah. However if you are not supporting the schach with the ties, but they are there merely as a precaution just in case there will be a strong wind, that is not considered being a support and it is permitted.
Chazon Ish 143-2 D:H U’lchen, Kovetz Halachos (Succos) 6-7.