Short answer: no tool can reliably show you an adult's incoming texts from outside his phone, and the app you saw advertised cannot do it on an iPhone at all. Every vendor that says otherwise is selling a screenshot, not a capability.
What "reliable" actually means here. Reliability comes from your own account, not from a hidden app. If he is on your family plan, the carrier portal lists the number, timestamp and length of every SMS and call on that line β metadata rather than content, but it answers "who" far more often than people expect, and it is the record that survives scrutiny because the network generated it. It costs nothing beyond the plan, and the request is a form in your carrier account, not a download.
Where the advertised app stops. Ultimate Phone Spy (ours) reads SMS, MMS and call logs from a phone you administer, with the person who uses it aware of the setup. It runs on Android 4.0+, Windows and Mac. It does not cover iPhone, there is no remote install, and it cannot pull messages from a passcode-locked phone it was never set up on β the system requirements page says so plainly instead of burying it.
The two cases that matter. A minor child's Android phone is the legitimate use: SMS tracking from $16/month annually, geofencing and web history alongside it. An adult partner without consent is not, and no product changes that β unauthorised access to stored communications is a Wiretap Act/ECPA offence in the US (18 U.S.C. 2510-2523), a Computer Misuse Act offence in the UK, and stalking-adjacent in most of the EU. We covered the longer version, including the court-order route, in this thread.