Am I correct in saying that my first line of action to prevent incontinence is not to cut back on fluids, but specifically fluids with caffeine?
Not really. Caffeine is a mild diuretic, but your problem is not "excess fluid" intake, or even things like caffeine stimulating your urge to urinate. Incontinence is usually anatomic (like stretching due to childbirth) and the solution is similarly anatomic (surgical support or repair). See a urologist or gynecologist; don't restrict fluids!