I recently signed up with the DailyPlate to track calorie intake and activity expenditure. For every calorie I burn, the program adds it back to my consumption bank. My question is, if I am on a 1800 calorie diet (the BMR/RMR for my goal weight), then burn 300 calories, should I be concerned with reconsuming those 300 calories to prevent "starvation mode"? I just seems counterproductive to me but I know that WW gives you "activity points" which allow you to eat more. Anyway, what are your thoughts on this?

All those numbers (including calories consumed) are, at best, rough estimates. Your best guide is your body. I'd eat 1800/day + moderate exercise for three full weeks, weighing weekly. Ignore the first weeks: that is your body adjusting. Looking at the next two, did you lose an average of 1-2 lbs a week? We your relatively sated, or were your having to control terrible hunger?

If you lost 1-2 lbs and weren't terribly hungry, keep doing what you were doing.

If you lost over 2 lbs and were terribly hungry, up your calories 100/day.

If you lost less than a lb, I'd cut back 100-200 calories/day and see what happens.

If you lost less than a lb and you were very, very hungry, change what you are eating: maybe more fiber, more vegetables, more protein, fewer carbs, something.

This is always an experiment. Figure out what your body needs.