Magento 1.9 multi site issues

I have 2 sites (Site A and Site B) which are run from one Magento 1.9 backend.
Product A is configured to be displayed on Site A and Site B.
Product B is configured to be displayed on Site A and Site B.

Site A shows product A and is searchable - it’s perfect.
Site B shows product A and is searchable - it’s perfect.

I add product B to the Magento Catalogue, reindexed everything and sent the changed to Algolia.

Site A shows product B and is searchable - it’s perfect.
Site B does not display product B and is not searchable.

Does anyone know why this would happen? I can only think there is a certain part of the index process which is not being run from the backoffice index refresh of Magento.

Hello @mksportscars,

that shouldn’t happen and the product should be indexed at both sites.
Can you post here a screenshot of the product’s store configuration?

Thank you!