In most cases you're right.
But the O.P. is correct....this doctrine is misunderstood by many and they continue to live their normal lives believing that their belief in Jesus will save them.
Be careful you don't judge others just because their external sanctification, which is what we see, isn't happening according to your ideal timeframe.
Some people's observable change happens quicker than others. Sometimes it can be sped up with discipline, other times it's just a matter of growth, etc. A good pastor, including one who teaches OSAS, doesn't neglect helping in his congregation's sanctification. An OSAS preacher who's doing his job correctly also understands that our faith isn't simply about going to heaven when we die.
Jesus NEVER said to just believe in Him and we'll be saved...
God's word teaches that we're
justified by faith, not by works.
God's word also teaches that without works, faith is dead.
The way these go together is by understanding that
regeneration is behind both faith and works.
Once-Saved-Always-Saved means, basically, that once one is born-again, they are permanently changed at their most core level, even if that change takes a while to show up. Post-regeneration, a person's indwelling sin (which is what we see when a Christian sins) is something that belongs to a part of them that isn't, strictly speaking,
them anymore.
This is why St Paul wrote that it is no longer he who sins, but rather the sin in him that does:
Romans 7:20-25
Now if I do what I do not want to do, it is no longer I who do it, but it is sin living in me that does it. So I find this law at work: Although I want to do good, evil is right there with me. For in my inner being I delight in God’s law; but I see another law at work in me, waging war against the law of my mind and making me a prisoner of the law of sin at work within me. What a wretched man I am! Who will rescue me from this body that is subject to death? Thanks be to God, who delivers me through Jesus Christ our Lord!
So then, I myself in my mind am a slave to God’s law, but in my sinful nature a slave to the law of sin.
This is also why the writer of 1st John said that Christians no longer sin, while also saying in the same epistle that if we say we have no sin we're deceived. That sin is external, while the regeneration affects our "inner being."
When one is born-again, sooner or later there is going to be fruit from that. So in that sense, it is true that it's not just a matter of believing. But that shouldn't be confused with our salvation being dependent on our works. That would violate other explicit teaching in scripture.
But what if the doctrine we trust goes AGAINST what Jesus taught? As does osas. THEN does our salvation come into question? Are we in danger as the O.P. says?
If God wants you saved, then sooner or later He will set you right.
Besides, there's a difference between being mistaken and being unrepentant. The disciples and other saints in the Bible frequently misunderstood God. It was God - the "author and perfecter" (Hebrews 12) of our faith - who saved them in spite of their misunderstanding. This is also why the Bible teaches things like predestination (see Ephesians 1). It's not ultimately up to us. That's why OSAS is true.