In an Hybrid configuration, while migration of Resource or Room Calendars to Exchange On-line works there are a few configurations that will need to be set with the help of Power Shell.
Recently I performed such a migration and found that while the Calendars were available to both Office 365 and on-premises users, there were a lot of issues with; Bookings, viewing details and notifications. In order to sort this out I had to run a few Power Shell commands against each affected Calendar.
Info on this command can be found here : set-mailboxcalendarfolder
Sets whether the calendar is published to external users
Set-MailboxCalendarFolder firstname.lastname@example.org:\Calendar -PublishEnabled $true
Sets the detail level users can view
Set-MailboxCalendarFolder -Identity “email@example.com:\Calendar” -DetailLevel FullDetails
Info on this command can be found here: set-calendarprocessing
Set this to correct an issue where users do not receive a confirmation on a successful booking. More info
Set-CalendarProcessing -Identity “firstname.lastname@example.org” -ProcessExternalMeetingMessages $True
Hope this helps!