Rule only runs when manually invoked

[Ellen]

The first (topmost) rule in my list is:

Apply this rule after the message arrives
with '** SPAM **' in the subject
and on this machine only
move it to the Junk E-Mail folder

This rule does not execute as I want when Internet mail
is downloading. If I manually run it, it works just fine.
(Our Internet email host has spam tools that insert '**
SPAM **'into the subject of suspect email.)

However, the last rule of my 5 rules is

Apply this rule after the message arrives
through the (e-mail address removed) account
and on this machine only
move it to the myemail folder

This one works perfectly. As mail is downloaded from the
Internet it is moved to the folder automatically. The
thing is, all the '** SPAM **' email is also going to
this folder. I want it to go to Junk Email. What do I
need to do to get this happen? (Could it be that the
email is going to Junk but the last rule is pulling it
back out and moving it to the myemail folder? )

Thanks for any suggestions!

Notes:
All my rules are client-only.

We do have an Exchange server but my Outlook is set to
pull down Internet email itself. I have an Exchange
account and two Internet email accounts. I am also in
several distribution lists for Exchange and Internet
email.