As specified in the linked article, they are deleted if you follow the steps listed:
"Delete texts and attachments in Messages
When you use Messages in iCloud, all of your text messages and the attachments you send and receive use your iCloud storage. You can make more space available when you delete texts and attachments—like photos, videos, and files—that you don't need anymore. Follow the steps for your device.
iPhone or iPad
To delete a message or attachment, follow these steps:
- In a message conversation, touch and hold the message bubble or attachment that you want to delete.
- Tap More.
- Tap
, then tap Delete Message. If you want to delete all messages in the thread tap Delete All, in the upper-left corner. Then tap Delete Conversation.
To delete an entire conversation, follow these steps:
- Swipe left over the conversation that you want to delete.
- Tap Delete.
- Tap Delete again to confirm.
Want to delete more than one conversation at a time? Open Messages and tap Edit in the upper-left corner. Then tap the circle next to the conversation and tap Delete in the bottom-right corner."
