You're definitely asking the right questions about the use of bulbs in your garden, and adding bulbs to your landscape is a great idea for several reasons!

Tulips are terrific spring-blooming plants. The label stating "Jan-April" is indeed referring to their flowering season. It's so broad of a timeframe since it depends on where in the country you are and when "spring starts".  If you research crocus, daffodils and tulips more closely, you'll find certain varieties flower "early", "mid-season" or "late". And, then you translate that to your climate where you live.

Tulips tend to diminish after their first time flowering unless you have cool summer soils, and squirrels eat the bulbs and deer love to eat the flower buds. Tulips are often planted among spring annual flowers so the tulips grow up among the lower annuals (like pansies) and flower. Tulips also are gret planted in clusters around hostas, since by the time the tulips' flowering ends, the hostas are starting to sprout and will soon mask the boring tulip foliage. Likewise, daffodil foliage is easily masks by other emerging perennials ornamental grasses or meadow forbs. Crocus often pops up through low groundcovers or in rockeries, or in dormant lawn turfgrass.

I'm sure a few others can chime in on the issues with placement of bulbs around shrubs, the need for foliage to ripen, etc. and other things to deal with concerning spring-flowering bulbs (there's also summer and fall flowering bulbs, too)!