Supercapacitors in series
There is no indication when using the SAB devices (likely the Maxwell balancing board you are using). It's based on balancing the leakage currents of the series connected supercaps and will not protect you from poor balancing at high charge current. Since you cap values can vary by more than 20% (datasheet) you will have unbalanced terminal voltages, so must provide this protection. 

Yes you can easily end up stressing a capacitor due to overvoltage.
If you are going to charge the capacitor string at say 10A (your PS in CC mode), then you must allow for the possibility that any one of the caps may enter overvoltage (whatever you select as the terminal voltage ..in this case 2.7V maximum). At that point in time you need to stop charging that capacitor so must shunt the 10A around the cap, which will stop it charging.
At 2.7V and 10A you obviously need to dissipate 27W in the shunt while the other caps continue to charge. 

Given you have 4 caps in series you will need a shunt balancer across each cap to protect it.
How you create your protection mechanism depends on what maximum charging current you want.   

For example if you set the maximum current at say 1A, then you only have to dissipate 2.7W in each shunt which would be much easier to design. Worst case you will have 3 of the 4 shunts active, so a total of about 8W. At 10A you may need to dissipate 80W worst case.  

There is some added complexity due to the ESR, but in the case of the caps you are using this is very low so can be almost ignored (max delta V would be 290mV @ 1A).