Question about Third order Butterworth Filter Design
Your LPF with 10Hz cutoff has transient reponse that will take about 0.5s (about 5*1/fc) to fully settle. That's what you are seeing.
For faster step-response settling you need to pick a wider filter with higher Fc.
Have a look here for the relationship between rise time and filter Fc:

Image from https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=9817
There are circuit tricks to get it to start at a desired known non-zero DC by initializing your filter to a desired &quot;reset&quot; state. Although this does not change the rise time, it does allow the circuit to start at a pre-fixed DC level immediately after a reset. (This requires additional analog switches and control circuitry)