You can be arrested for DUI even after you are parked and out of the car. It still has to be proven that you drove, however, that can be done in several ways. The officers could have seen you drive, there may be a citizen call identifying the car and/or driver, there may be circumstantial evidence that you drove. The other way to prove driving is by you admitting driving or anyone with you saying you drove. Additionally it has to be shown that you did not drink after driving so that any blood alcohol level can be extrapolated back to time of driving.
They can also show it if circumstantially by the fact the engine is warm, the keys are in your pocket, the seat adjustment,…and other circumstances that show you drove to the location and did not drink after arriving. The officers can contact you to investigate if there is a citizen call or other information justifying further investigation. The stronger the “driving issue” the better then disposition that can be negotiated, and the better chance you have at trial if it goes.