If it's a septic tank (a type of treatment) as opposed to a cess pit (merely a storage tank) then, yes, it should look full.
A cess pit is just a storage tank and has no outlet, so, unless it's leaking, when it gets full you will have to empty it or it overflows. with mildly unpleasant consequences. Addition of rainwater will make it fill up quicker, therefore costing you more for emptying.
A septic tank is a treatment system that anaerobically digests the sewage. Once it is filled, further inlet flow of sewage displaces treated liquor out of an outlet pipe to a soakaway. Hence it will always look full, but that does not mean it needs emptying. As time goes on, it will become more full of sludge leaving less room for liquor, until such time as the effluent coming out of it is sludge rather than liquor. At this point it needs emptying, otherwise the soakaway will become heavily polluted and / or blocked, again with unpleasant (and costly) consequences.
The time taken for it to fill with sludge and require emptying will depend on the size of the tank and the amount of waste it receives, and could be anything from one to several years, but I guess a couple of years would be average.
Whilst it is probably not good practice to allow rainwater / downpipes to feed into it, this will only serve to dilute the liquor within the tank and will not cause it to need emptying any sooner, as rainwater contains no significant organic material and so will not enhance the sludge production in any way