You finish a message tonight and want it to arrive during a colleague's morning. Choosing 09:00 is only useful if you know which time zone that means. Gmail uses the time zone in which you schedule the message, and Google says sending can happen a few minutes after the selected time.
Check the saved message
On a computer, open the arrow beside Send and choose Schedule send. Check the date as well as the hour. Then open Scheduled in the left panel and inspect the saved message: recipients, attachment or link, and sending time.
For a simple example, suppose your zone is UTC+2 and your colleague's is UTC+1 on that date. Your 09:00 is their 08:00. To target their 09:00, the corresponding time for you is 10:00. Check the offsets for the actual date; seasonal clock changes can alter the difference.
A changed plan needs a new schedule
To edit a waiting message, open it in Scheduled and cancel its send. Gmail returns it to drafts. Make the changes and schedule it again; leaving the edited draft open does not restore the old schedule.
Before closing the task, confirm that the replacement appears in Scheduled and no outdated version remains queued. A link may lead to a document that has changed since you wrote the email, so open that too.
After the planned time, check Sent and any failure notice. A sent message is not proof that the recipient read it. For a deadline that depends on an exact minute, allow for the documented sending delay.