In theory, not until next year - these usually start flowering in April or May, and go on for about 4 weeks. They do well in shadier spots, because they like damp soil conditions - if you only planted them three weeks ago, they do need regular watering after all the dry weather we had until recently, because the soil would have been pretty dry in the top 10 inches, which is where your pot shaped roots will be. Without sufficient water, plants will not maintain their flowers in order to survive. Keep them well watered and you might be lucky, they might put out a couple more plumes.

Don't expect much the 1st year with perennials. The 1st year they sleep, 2nd year they creep, 3rd year they leap. They just need time to acclimate & settle into their new environment. Keep the ground moist so they develop a nice healthy root system. Work in some rich organic compost & keep the ground evenly moist. Mulching will aid in doing this.

Your Astilbe,if kept sufficiently well watered, will grow and flower even better next year than they did this, Iceland 17.

welcome to GoY Iceland17
the sudden heatwave will have speeded up the decline in the flowers. as already said they like plenty of water and some shade.

I consider this plant a bog garden plant; it loves to keep its feet wet.

mine is growing next to the overflow pipe from the pond.
The dead flower spikes look good all the way through the season too. especially when frosty.
the goldfinches like the seed too.