ब्रह्मशब्देन स्वभावतः निरस्तनिखिलदोषः अनवधिकातिशयासङ्ख्येयकल्याणगुणगण: पुरुषोत्तमोऽभिधीयते।
All names are epithets of ब्रह्मन् who is conceived as above. So, according to
सर्वश्री-रामानुजाचार्य, the names viz., शिव, शङ्कर, इन्द्र and others in their etymological sense speak of ब्रह्मन् who is स्वभावतः निरस्तनिखिलदोषः and अनवधिकातिशयासङ्ख्येयकल्याणगुणगण: and पुरुषोत्तमः
The philosophical idea behind the above conception is - "ब्रह्मन् is वाच्य", meaning ब्रह्मन् is directly expressible by words (all words belonging to the domain of लौकिक & वैदिक)
Coming to your *core questions* of how Shiva is to be worshipped in that sampradaya and why followers of that sampradaya do not visit Shiva temples, I am afraid, I am not competent to answer,
The text quoted above may hold an answer, but I defer it to experts belonging to the sampradaya.
Thank you and Best regards,
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