Ah, sorry of course you're right.
So, on Box1 you need a way to run script-2
only when script-1 on Box2 is finished.
I can see 2 ways to do this. (Ok, it's ten-o-clock in the evening, I've worked hard and had 2 glasses of wine. I still know what I'm doing but please keep that in mind, I might miss some details.)
1) Scp the other way, meaning you put everything in one script on remote host.
You already have keys set up, so all you need do then is remove password prompting from box2 -> box1.
2) A bit more complicated, but also more elegant if you ask me:
a) Run script-1 on Box1, the one that starts a tarball-creating on Box2. Put the tarball in a dedicated directory (from now on called "DDIR") on Box2.
b) On Box2, use
inotifywait to watch DDIR with "close write".
Make a script on Box2 that uses inotifywait so that when a file is written to DDIR a file is created with name "tarball_complete".
c) On Box1, create a script that watches for this file on Box2, and downloads the tarball when the "tarball-complete"-file exists.
Easiest is to make it a cron-job, or you could have a loop in a small script to check for that file.
Of course, you'll have to provide your password every time the script is checking. If I were you I'd run those scripts under a special, very restricted user-account and use only ssh-keys.