We pronounce it じょう
like in Example 1 because we have 上
without any particle between it and the previous word, and it simply means 'on'.
In Example 1, it kind of works if we call it when
, but in general, 上
is used as a suffix to mean as a matter of sth
. Its literal meaning is
Cautions as a matter of usage
or even better, precautions
. That's what happened in Example 1.
But you are confusing the order of words in Example 2. This 上 is not the suffix for 使用
, thus the translation when using
or as a matter of using
is incorrect.
It is right after the word computer name
. That's a thing. It should mean 'on'.
Also, account name
is a name of somebody, so that の
works as a case particle for indicating ownership.
computer name 上{じょう}で使用{しよう}している account name の Firefox
Account name's Firefox running on computer name
Edit: I found out that this phrase can be interpreted 2 ways. The first one is shown above. The other is:
The Firefox running on account name on computer name
It's how we interpret the account name part. Firefox has a system that allows multiple profiles to be made in one installation like chrome does, so grouping account name の Firefox
makes sense. But if you think of, for example, a school, it is possible that account name
means your school account and that it can be used to log in to any computer in your school. Thus, grouping computer name 上で使用している account name
also makes sense.