You can't use a fake time list, you will need to use the real time list as you did in the SYS Time module. Now, if you must you the fake/custom time that you have for reporting reasons, then we can do a mapping to get the data there after you use the module with Real Time.
Re: INCREMENTAL CALCULATION AND CONDITIONL FORMATTING
i think it would be way too much complicated to use Previous or any time dimension related function since we use pretty much only customisezd time dimension and changing this will take some time; Do you perharps know a way to still implement the calculation without using a time dimension? something like if starting date= january then total allocation - january's allocation ELSE previous cell - current total allocation ".
Short answer, no as previous() only works with the Time dimension. Now, what I suggest is to do it the way I recommended in the above and then have a mapping module from your custom time to native time which you can use for reporting.