Most of the suggestions on the web refer to using the jigsaw for cutting patterns. It is the ideal choice for this work as some patterns are intricate with arcs and what not.
What you could do with the jigsaw is use your template as a guide. If your arcs or curves are simple enough you can shift the template down from where the cut will be. This might be difficult depending on the plate of your jigsaw and angles in your design.
That does not mean you are limited to just the jigsaw and the hand cramps that might ensue. Depending on your pattern you might be able to use some other tools to do the work as well.
The jigsaw cuts a full arc across the board and then the mitre saw cuts the 45 degree angle. Yes you could have done this all with the jigsaw but this is cleaner and faster. The pencil mark on the saw is a guide so you don’t need to measure every time.
A simple pattern like that could almost be done just with a circular saw. I doubt that is your pattern but one of the cuts might be.
You could make a simple jig for the saw using another board as a cutting guide.
Pattern Bit on a router
If your boards are thin enough, and you have a appropriately sized bit, you might be able just to use a pattern bit on your router (assuming it’s big enough). I have never tried a router as of yet but depending on how many cuts you need to make this might be over-kill for the router.
Even if your bits were long enough you could flip the board and template to cut from both sides. In theory giving you that perfect cut you are looking for.
You didn’t show us what you are doing. Hopefully there might be a way of incorporating other tools into your template to help with that repeatable precision you are looking for. Much like Caleb suggested your jigsaw and pencil will be your main tools here.