How to set a Slack reminder only to notify a subset of the people in the channel

Slack will only notify the first user you mention in the remind command.

Slack's reminder command supports only Users and Channels so you cannot create a group to notify a large group of people.

You will probably have to create a separate channel to notify them or create a bot using slack that does that if you want to create a special integration for that

If it is a recurring group of people that you usually want to notify together, you can add them to a group and notify the group.

Slack User Group Documentation

Official Source saying /remind supports groups