Breaking it down for you from your link:
- Do you have an eligible UK short stay visa?
Yes you do
- Does your visit to Ireland end before your permission to stay in UK ends (this is granted by an UK immigration official when you pass through UK immigration)?
You don't yet have this information, but let's assume they grant you the stay as you planned. So, yes.
- Was your passport issued by one of the countries listed in the list below?
India is listed, so yes.
By all indications from the official website to which you have also linked, you are indeed able to do this with the UK visa without additional need for an Ireland visa.
This is also supported by the following:
Travel between Ireland & UK using a single UK-Irish visa
You can visit Ireland and the United Kingdom using a single visa issued by either country, if you are a Chinese or Indian citizen. For instance:
You can visit the UK (including Northern Ireland) without applying for a UK visa, if you have an Irish Visit (Tourist) Visa.
You can visit Ireland without applying for an Irish visa, if you have an eligible UK (short stay) visitor visa.
You can travel an unlimited number of times between each country with either visa, for as long as it is valid.
Read how this works under the British-Irish Visa Scheme.