Hours which are past midnight are suffixed with next day date. In Panchang day starts and ends with sunrise.
Most of the customs and rituals observed during Shardiya Navratri are also observed during Ashadha Gupta Navratri. Ghatasthapana Muhurta is more popular during Shardiya Navratri but it is also needed during Ashadha Gupta Navratri.
Ghatasthapana is one of the significant rituals during Navratri. It marks the beginning of the nine days Durga Puja. Our scriptures have well defined rules and guidelines to perform Ghatasthapana during a certain period of time at the beginning of Navratri. Ghatasthapana is invocation of Goddess Shakti and doing it wrong time, as our scriptures forewarn, might bring wrath of the Goddess Shakti. Ghatasthapana is prohibited during Amavasya and night time.
The most auspicious or Shubh time to do Ghatasthapana is first one third of the day while Pratipada is prevailing. If due to some reasons this time is not available then Ghatasthapana can be done during Abhijit Muhurta. It is advised to avoid Nakshatra Chitra and Vaidhriti Yoga during Ghatasthapana but those are not prohibited. The most important factor to consider is that Ghatasthapana is done before Hindu midday while Pratipada is prevailing.
We also consider Lagna and try to include Dvi-Svabhava Lagna (द्वि स्वभाव लग्न) into calculated Muhurta. During Shardiya Navratri Dvi-Svabhava Lagna Kanya prevails during sunrise and if suitable we take it for Ghatasthapana Muhurta.
The factors which are prohibited for Ghatasthapana are afternoon, night time and any time beyond sixteen Ghatis after sunrise.
Ghatasthapana is also known as Kalash Sthapana or Kalashsthapana. You might also be interested in complete Ashadha Gupta Navratri Calendar.