Answer: Hybrid teas actually thrive with a severe pruning. In the Phoenix area, we prune in January-February to prepare for the major bloom period in April. Since you already pruned and the bushes are in bloom, do not do any further cutting back. Another lighter pruning is sometimes done in mid-September to prepare for the second bloom period in fall, but this is more of a "clean up" than severe structural change.
Cut back only about 1/3 of the bush at a time. Here are the basics: In the spring, remove the dead and damaged canes as far back as necessary. Then, remove any suckers that arise from below the graft union, if there is one (the swelling near the base of the plant). Next, select the healthiest canes (thicker and bright green) and cut off the rest. If your roses are just a couple of years old, save about 3-5 canes. Save more on older plants. Lastly, cut the flowering canes back by one-third to one-half. Make your cuts about 1/4" above an outward-facing bud.
Proper watering and fertilizing will encourage growth. Water should soak 2 feet deep, with fairly consistent soil moisture. During cool months, that's usually about once a week watering, depending on soil type and climate. As temperatures warm in spring (and fall) it's about 2 or 3 times per week. In the midst of summer, 3 or 4 times, or maybe even daily if the roses are in a difficult situation, such as next to heat-retaining hardscape.
If you didn't include slow-release fertilizer when you planted, use a slow-release product every 6 weeks during the growing season. Most local rosarians taper off fertilizer during the heat of summer as it's too stressful for the plant. Resume again in September and taper off in mid-October for winter. Resume again after pruning in January.
There are hundreds of rose varieties, so without seeing, it's hard to hazard a guess. For identification, I recommend you visit the Mesa Community College Rose Demonstration Garden. It is an AARS test garden with hundreds of varieties, which are coming into their peak bloom season. MCC is just off the 60 Freeway, at Dobson and Southern.
Finally, there is an upcoming rose garden tour that you might enjoy from the Mesa-East Valley Rose Society. For info, check the website at http://www.roses4az-mevrs.org.
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