For a booking here, time zone means Amsterdam time, CET in winter and CEST in summer; every start in the thread is read on that clock, whatever your phone shows.
In winter Amsterdam runs on Central European Time, UTC plus one; from the last Sunday in March to the last Sunday in October it switches to Central European Summer Time, UTC plus two. Every time the office writes in a thread, and every time it reads, is on that clock.
Most errors happen before the traveller lands. A passenger in a lounge in Dubai or Chicago types "tonight at nine" and could mean three things: nine where they are sitting, nine on their body clock, or nine in Amsterdam. Phones add to the confusion by switching zones on landing, which quietly moves calendar reminders, and by showing timestamps in whatever zone the handset thinks it is in. The office reads "nine" as 21:00 Amsterdam time, and if the message arrives from a distant country code it will usually check. You can remove the question entirely by writing the zone: "21:00 Amsterdam time, Tuesday".
Overnight flights add a second trap, the date. A request for "Wednesday night" sent from a city where Wednesday has already begun can be read a day out. For a late start, name both the date and the hour, and make clear which side of midnight it falls on: "00:30 in the early hours of Thursday" leaves nobody guessing.
Every booking names an hour and a date, and that fixed time is what the office holds for you. A booking confirmed for the wrong day because of a zone slip is still a confirmed booking, and cancelling it follows the ordinary rule: the deposit is not returned. Read the confirmation back once, in Amsterdam time, before you pay. The journal piece on booking across time zones works through examples, and the jet lag entry covers the body-clock side.
One hour EUR 180 through to eight hours at EUR 1,250. Forty to sixty minutes anywhere in the centre; the Schiphol airport hotels by arrangement.