Please post your environment; operating system, version, etc.
To make anything start at boot time you (or the install routine) will need to enter it in a startup script somewhere (eg, a file in /etc/rc3.d), unless you're running an O/S that's clairvoyant you will need to tell it what to do.
Well I'm not familiar with LinuxMint 16 64bit but the multi-user startup scripts are usually in /etc/rc3.d (or perhaps in your O/S /etc/rc.d).
Take a look in there and list the files present. Is there a Tomcat? Use grep to search for it. If the command you used entered the required script you should see it (or at least a link to the file elsewhere).
If all else fails you could simply create a file SnnTomcat for example and put your Apache start command in there (where nn is a number setting the appropriate position in the boot sequence). Make the script executable.
I expect another member who knows LinuxMint better will respond and help you out shortly.
The problem might also be the init level, type who -r to know what is your default level... then be sure the start link is in that rc.*d and put the stop in one level lower...
The first question that comes to mind is "have you looked at your various system and error log files to see if there are any clues there?"
Or have you considered adding a simple logging statement to your script to test to see what is going on when the script executes during boot time (or if it is even being executed all all)?
My experience is that logging (printing) is just about the most valuable debugging tool available.
You installed this package using a documented procedure.
You can start Tomcat manually. Good!!!
The procedure created a script in /etc/rc2.d/S20tomcat7 but it doesn't run at boot time.
As per my post #12 you can test this manually to see any errors.
Pay particular attention to VBE's comment about run levels.
It could be that the script in rc2.d is the stop script, and the start script is in rc3.d, I don't know LinuxMint. Perhaps rc2.d is start and rc1.d is stop.
Take a look around and see.
Then, logged in as root you should be able to start and stop Tomcat from the command line using these scripts. Post any errors.