The strategies should rebalance once every month (except MYRS which is twice/month). No need to adjust weights. So one trade a month is all you have to do.
The backtester assumption is that trades happen on close price on the day before the 1st of the month (ie January 31st). This is slightly different than trading on the 1st but it is not a critical difference according to our tests.
It is possible to trade on the last day of the month using QuantTrader by downloading intraday data before the close and issuing signals at your own workstation/laptop. I suggest that you download and use our 30-day free trial of QuantTrader. You can then check exactly how our strategies work and even backtest instantly different rebalance days (+-1,2,3).
https://logical-invest.com/quanttrader-application/