The paper's sieve bound for integers with large least prime divisor

Let $a,b$ be positive integers with $\gcd(a,b)=1$, let $x$ and $y$ be positive real parameters, and let $p(n)$ denote the smallest prime divisor of the integer $n$. Sieve bound conjecture. The number of integers $n\leq x$ satisfying $n\equiv a\bmod b$ and $p(n)>y$ should satisfy

$$\#\{n\leq x:n\equiv a\bmod b,\ p(n)>y\}\ll\frac{x}{b}\prod_{\substack{p\leq y\gcd(p,b)=1}}\left(1-\frac{1}{p}\right).$$

The source calls this its second conjecture and uses it to bound prime-testing costs after sieving; no resolution is given.