The application I am trying to run is the ATG Control Center (ACC) -
http://www.atg.com. It is a remote java app that connects to an server application over RMI. It is a pure java app so I don't believe it was running under Rosetta.
I can't tell from the ATG website how the ACC app is deployed. My guess is that it's a Java Web Start application, not a downloaded and locally-run app-bundle.
Assuming it's a Java Web Start application, then they have full control over which Java version it requires. This control is absolute. If they say it requires a version of Java 1.3, then that's what it requires and there's not much you can do about it, except complain to ATG that they should support newer Java versions (1.3 is ancient, and requiring it and ONLY it is ridiculous).
For what it's worth, the requirement for a particular Java version will be given in the .jnlp file of the app's provider. Without seeing that, it's impossible to say whether they really are requiring 1.3 or not. And without the URL of that .jnlp file, there's no way to see what it contains.
On the question of Rosetta, the JVM itself would run under Rosetta, and the pure Java app would then be run under the JVM. The JVM is just a program written in C and C++; it's not magic.
If this is happening, you can observe it in Activity Monitor.app, found in your /Applications/Utilities folder. Simply launch the app, run Activity Monitor, then scroll the list of processes sideways to show the "Kind" column. If it says "PowerPC" on the line for your app, then it's running under Rosetta. If it doesn't say "PowerPC", then it's not running Java 1.3. Truly, Rosetta is the only way to run Java 1.3 under Tiger on an Intel Mac.
Finally, you still haven't said what OS version you were running when the ATG app was working.