Is the custom value a new field in TypeForm, or the same field in TypeForm?
If it’s a new field, it would show up as a different field in Airtable.
If it’s the same field, then Typeform probably doesn’t have the ability to add new options into a multi select field. In that case, you would need to use a tool like Integromat to act as the middleman between TypeForm and Airtable, and be sure to turn on the “Smart Links” feature in Integromat to enable the adding of new multi-select options in Airtable.
Alternatively, you could switch away from TypeForm and use the form by MiniExtensions: