Support confirmed to me months ago that this is a bug. There is no way to turn shipment notification off.
On the order page, if you select "Shipstation Notifications: Do not send email" it still sends an email. This is regardless of whether it's an imported (through the API) or manually created order.
The workaround is to edit the customers email & put in a bogus email address (you can put in your own email address & you'll see that you get the shipment notification email every time) Doing this causes other problems for us though because email is a unique ID in our integrated systems.
We sell some things on ebay. Sending these notifications results in a "Violation of Messaging Policy" email excerpt:
Please review our messaging policy
We wanted to let you know that some of the emails you sent to your buyers this week couldn’t be sent because they violated our member-to-member contact policy. We know how important it is to communicate with your buyers, so we wanted to remind you that your eBay emails should only be about your eBay transactions and can’t be used for promotions outside of our marketplace.
I'm always surprised at how long it takes shipstation to fix major glaring bugs.