Custom functions set Modified by to script owner
As a ZOHO administrator, I have created custom scripts that run in various situations like updating a field, let's say in the Accounts module.
In such cases the "Modified by" field is set to my name, although the record was modified by someone else. I suppose this is because I'm the script owner.
How can I make it keep the name of the person who actually modified the record?
This raises another question: if there are several automation actions triggered by the same event, what is the order of their execution?
I'd also like to know if rules triggered by "Create or Edit" of a record include "Field Update" or not.
That is, if I have a rule for editing a record, and one for updating a field in the same record, will both rules be triggered, and in which order?
Thanks.

Moderation Update: