I have an article here for you that can describe the preferences that you should check for to make sure Safari performs this operation as you expect:
To set your homepage, follow these steps:
- In Safari select Safari > Preferences… > General (toolbar)
- Type or paste the homepage URL in the "Homepage:" field
- If you want your homepage to open in a new Safari window, select "Homepage" in the "New windows open with:" pop-up menu.
- If you want your homepage to open in a new Safari tab, select "Homepage" in the "New tabs open with:" pop-up menu.
Important: With Resume enabled, Safari will not always open with your homepage, even if in Safari Preferences you have selected "Homepage" in the "New windows open with:" pop-up menu. To open your Homepage under these circumstances, hold down the shift key when you open Safari.
You will want to specifically choose the options you wish to have in steps 3 and 4 above to directly address your question. Thanks for coming to the Apple Support Communities!