Answer: It is better to plant the mums as early as you can to give them more time to become rooted -- that way they will have a better chance of overwintering successfully. Usually mums do better and bloom more if divided each spring, so you will probably want to do that. In the course of a summer one mum can grow to be a foot wide or wider, assuming all goes well. (Depends partly on what variety you have.) And, mums need a rich soil that is evenly moist yet well drained plus a location that is in full sun. Direct sun all day is good, or a minimum of a half day including the hour of noon.
Since you mention impatiens, I should really point out that if the site is shady enough for impatiens to be happy, then it will be too shady for mums to grow vigorously and bloom well. So this may not be the place for your mums and tulips.
Tulips also bloom and grow much better in a full sun location, they will also come up and bloom earlier in more sun. Many tulips usually do not perennialize all that well, so I would not plan on keeping them for more than next spring's bloom unless you have some of the species tulips or cottage tulips that are reliably long lived.
Assuming you have a sunny spot, I would plant the tulips to the back of the bed about four inches apart in drifts or irregular groups of say five or seven. Then I would plant the mums in front of them. The spacing for the mums should just look nice for now, they won't get bigger this year. Next spring you can divide the mums and then plant them about a foot apart to allow them space to grow over the summer. They will at least distract the eye from the fading tulip foliage but will not hide it. To hide it you would need some taller foliage from faster growing perennials such as daylilies. Daylilies need at least a half day of sun, as would the tulips if you want ot try to mature the foliage and keep them going.
I hope this helps.
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