I flew this is the other direction in J a few months ago. Meal services were good on each leg and the cabin was almost empty between TPE and MNL as many pax disembarked in TPE. KL is not allowed pick up new pax in TPE.
You basically exit the plane, there's a sign with a cardboard cutout KLM lady with Manila on it. Go through security - you will be one of the first through as you are flying in J, which means you will have at least 30 minutes to spend in the China Airlines lounge. The lounge is decent. Several other pax from the KL flight used it although I think I was the only one who dared to have a shower. Yes, I had time for a shower and a quick snack during my time in the lounge.
A CI staff member entered the lounge calling pax for the flight to Manila although we were still maybe 45 minutes before departure and the gate was only a 2 minute walk from the lounge. I moved quickly towards the gate but when I arrived boarding was only just starting, so I think I could easily have spent another 15 minutes in the lounge - there was no need to rush to the gate.