Suppose I want to monitor with a bot a given long dormant address A, so that if it sends a transactions to some other address B, say tomorrow at 10:09:26, then my bot will also send a transaction to B at the same exact time,so that in the blockchain it is impossible to say which one is earliest.
No It does not work that way, transactions are included in blocks and if your bot detects the address has already sent the transaction, meaning it has received at least 1 confirmation, then even if you prompt your system to send some bitcoin to the address at the time of notification, the network delay would have its effect and every new block has a delay of approximately 10 minutes before it is mined and it may be longer if there is higher network difficulty in finding the valid hash to confirm the transactions in the new block.
Like the other speaker said, there is still no guarantee your transaction would be included in the next block although you would be at advantage for it to be included if you use higher fees, and there is no specific time frame for your transactions to be confirmed, it depends on the action of the miners and the network difficulty at that point, but sending transactions concurrently with a speed of light
to address B after your bot must have been notified of the first transaction
from address A being confirmed is not possible in the bitcoin network.